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# One used-car salesperson receives a commission of \$ 200 plus 4 percent

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Math Expert
Joined: 02 Sep 2009
Posts: 50042
One used-car salesperson receives a commission of \$ 200 plus 4 percent  [#permalink]

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13 Dec 2015, 04:53
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Difficulty:

15% (low)

Question Stats:

79% (01:44) correct 21% (02:38) wrong based on 106 sessions

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One used-car salesperson receives a commission of \$ 200 plus 4 percent of \$ 1,000 less than the car’s final sale price. Another car salesperson earns a straight commission of 6 percent of the car’s final sale price. What is the final sale price of a car if both salespeople would earn the same commission for selling it?

A. \$ 5,000
B. \$ 6,000
C. \$ 8,000
D. \$ 10,000
E. \$ 12,000

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Joined: 20 Feb 2015
Posts: 793
Concentration: Strategy, General Management
Re: One used-car salesperson receives a commission of \$ 200 plus 4 percent  [#permalink]

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13 Dec 2015, 13:01
let s1 and s2 be the commission earned by the two salesperson
as per the question,
s1=200+0.04(x-1000) (where x is the sp of the car)
s2=0.06x
also
s1=s2
or,
200+0.04(x-1000)=0.06x
200+0.04x-40=0.06x
0.02x=160
x=8000
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Re: One used-car salesperson receives a commission of \$ 200 plus 4 percent  [#permalink]

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15 Dec 2015, 17:14
Hi All,

This question can be solved by TESTing THE ANSWERS.

We're given the pay rate of two different salespeople who sell cars:
1) A commission of \$ 200 plus 4 percent of \$ 1,000 less than the car’s final sale price.
2) A straight commission of 6 percent of the car’s final sale price.

We're asked for the final sale price of a car if both salespeople would earn the SAME commission for selling it?

1st salesperson = \$200 + .04(6,000 - 1,000) = \$200 + .04(5,000) = \$200 + \$200 = \$400
2nd salesperson = .06(6,000) = \$360

These totals are NOT the same, so we can eliminate B. Looking at the two pay 'formulas', we can see that the 2nd salesperson will make more money than the 1st when the price of the car increases to a significant level, so we need a price that is HIGHER than \$6,000. Since the difference in pay is relatively small in Answer B, we're likely looking for a number that is fairly close to \$6,000 though...

1st salesperson = \$200 + .04(8,000 - 1,000) = \$200 + .04(7,000) = \$200 + \$280 = \$480
2nd salesperson = .06(8,000) = \$480

These totals are the SAME, so this must be the answer.

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Intern
Joined: 27 Oct 2015
Posts: 26
Re: One used-car salesperson receives a commission of \$ 200 plus 4 percent  [#permalink]

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15 Dec 2015, 23:03
Let the price be x

[4% = 1/25 and 6% = 3/50]
200 + (1/25)(x - 1000) = (3/50)x

Multiply throughout by 50

10000 + 2x - 2000 = 3x
x = 8000
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Re: One used-car salesperson receives a commission of \$ 200 plus 4 percent  [#permalink]

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16 Dec 2015, 00:24
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

One used-car salesperson receives a commission of \$ 200 plus 4 percent of \$ 1,000 less than the car’s final sale price. Another car salesperson earns a straight commission of 6 percent of the car’s final sale price. What is the final sale price of a car if both salespeople would earn the same commission for selling it?

A. \$ 5,000
B. \$ 6,000
C. \$ 8,000
D. \$ 10,000
E. \$ 12,000

Let the final sale price be x. Then we have (x-1000)*(4/100) + 200 = x*(6/100). By multiplying 100 to both sides we have 4x-4000 + 20000=6x. So we get 16000=2x ---> x=8000

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Re: One used-car salesperson receives a commission of \$ 200 plus 4 percent  [#permalink]

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10 Apr 2016, 12:42
test for various answer options one by one
test for option A
200 +0.04*(5000 - 1000) is not equal to 0.06*5000
test for option B
200 +0.04*(6000 - 1000) is not equal to 0.06*6000
test for option C
200 +0.04*(8000 - 1000) is equal to 0.06*8000 = \$480
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Re: One used-car salesperson receives a commission of \$ 200 plus 4 percent  [#permalink]

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25 Oct 2017, 07:20
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Re: One used-car salesperson receives a commission of \$ 200 plus 4 percent &nbs [#permalink] 25 Oct 2017, 07:20
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